Path Integral Representation of Generalized Nonlinear Schrödinger Equations -- Application to Optical Soliton Problems.

The nonlinear Schrödinger equation (NLSE) is one of the partial differential equations appearing in a number of research areas including mathematics, physics, engineering, and biology. Its applicable area is quite wide. In this paper, as a solution method for an NLSE accompanied with modification or perturbation (generalized NLSE), the - integral method (NM) is used. The basic concept, formulation, and actual numerical calculation algorithm are described. The NM introduced by Feynman is a nonrelativistic quantum mechanical formulation based on the Lagrangian font Since the final formula obtained in this paper takes a standard Fourier transform type, it is possible to use the fast Fourier transform (FFT) so that a quantum jump in numerical efficiency has been attained. it should be noted that only one Fourier transform operation is needed per unit propagating section. As a generalized NLSE, a set of coupled nonlinear Schrödinger equations with a perturbation is considered. As a specific example of application, numerical results for optical solitons are presented. [ABSTRACT FROM AUTHOR]